Evidence for two separate energy gaps in underdoped high-temperature cuprate superconductors from broadband infrared ellipsometry

Analogies of phonon anomalies and electronic gap features in the infrared response of Sr14-xCaxCu24O41and underdoped YBa2Cu3O6+x

We present an experimental and theoretical study which compares the phonon anomalies and the electronic gap features in the infrared response of the weakly coupled two-leg-ladders in Sr14-xCa_xCu₂₄O₄₁(SCCO) with those of the underdoped high-T_csuperconductor YBa₂Cu₃O6+x(YBCO) and thereby reveals some surprising analogies. Specifically, we present a phenomenological model that describes the anomalous doping- and temperature-dependence of some of the phonon features in thea-axis response (field along the rungs of the ladders) of SCCO. It assumes that the phonons are coupled to charge oscillations within the ladders. Their changes with decreasing temperature reveal the formation of a crystal (density wave) of hole pairs that are oriented along the rungs. We also discuss the analogy to a similar model that was previously used to explain the phonon anomalies and an electronic plasma mode in thec-axis response (field perpendicular to the CuO₂planes) of YBCO. We further confirm that an insulator-like pseudogap develops in thea-axis conductivity of SCCO which closely resembles that in thec-axis conductivity of YBCO. Most surprisingly, we find that thec-axis conductivity (field along the legs of the ladders) of SCCO is strikingly similar to the in-plane one (field parallel to the CuO₂planes) of YBCO. Notably, in both cases a dip feature develops in the normal state spectra that is connected with a spectral weight shift toward low frequencies and can thus be associated with precursor superconducting pairing correlations that are lacking macroscopic phase coherence. This SCCO-YBCO analogy indicates that collective degrees of freedom contribute to the low-energy response of underdoped highT_ccuprates and it even suggests that the charges in the CuO₂planes tend to segregate forming quasi-one-dimensional structures similar to the two-leg ladders, as predicted for the stripe-scenario or certain intertwinned states.

Field-dependent specific heat of the canonical underdoped cuprate superconductor [Formula: see text]

The cuprate superconductor [Formula: see text], in comparison with most other cuprates, has a stable stoichiometry, is largely free of defects and may be regarded as the canonical underdoped cuprate, displaying marked pseudogap behaviour and an associated distinct weakening of superconducting properties. This cuprate 'pseudogap' manifests as a partial gap in the electronic density of states at the Fermi level and is observed in most spectroscopic properties. After several decades of intensive study it is widely believed that the pseudogap closes, mean-field like, near a characteristic temperature, [Formula: see text], which rises with decreasing hole concentration, p. Here, we report extensive field-dependent electronic specific heat studies on [Formula: see text] up to an unprecedented 400 K and show unequivocally that the pseudogap never closes, remaining open to at least 400 K where [Formula: see text] is typically presumed to be about 150 K. We show from the NMR Knight shift and the electronic entropy that the Wilson ratio is numerically consistent with a weakly-interacting Fermion system for the near-nodal states. And, from the field-dependent specific heat, we characterise the impact of fluctuations and impurity scattering on the thermodynamic properties.

Optical studies of high-temperature superconducting cuprates

The optical studies of high-temperature superconducting cuprates (HTSC) are reviewed. From the doping dependence of room temperature spectra, a dramatic change of the electronic state from a Mott (charge transfer) insulator to a Fermi liquid has been revealed. Additionally, the unusual 2D nature of the electronic state has been found. The temperature dependence of the optical spectra provided a rich source of information on the pseudogap, superconducting gap, Josephson plasmon, transverse Josephson plasma mode and precursory superconductivity. Among these issues, Josephson plasmons and transverse Josephson plasma mode were experimentally discovered by optical measurements, and thus are unique to HTSC. The effect of the spin/charge stripe order is also unique to HTSC, reflecting the conducting nature of the stripe order in this system. The pair-breaking due to the stripe order seems stronger in the out-of-plane direction than in the in-plane one.

Universal self-field critical current for thin-film superconductors

For any practical superconductor the magnitude of the critical current density, Jc, is crucially important. It sets the upper limit for current in the conductor. Usually Jc falls rapidly with increasing external magnetic field, but even in zero external field the current flowing in the conductor generates a self-field that limits Jc. Here we show for thin films of thickness less than the London penetration depth, λ, this limiting Jc adopts a universal value for all superconductors-metals, oxides, cuprates, pnictides, borocarbides and heavy Fermions. For type-I superconductors, it is Hc/λ where Hc is the thermodynamic critical field. But surprisingly for type-II superconductors, we find the self-field Jc is Hc1/λ where Hc1 is the lower critical field. Jc is thus fundamentally determined and this provides a simple means to extract absolute values of λ(T) and, from its temperature dependence, the symmetry and magnitude of the superconducting gap.

Nonlinear lattice dynamics as a basis for enhanced superconductivity in YBa2Cu3O6.5

Terahertz-frequency optical pulses can resonantly drive selected vibrational modes in solids and deform their crystal structures. In complex oxides, this method has been used to melt electronic order, drive insulator-to-metal transitions and induce superconductivity. Strikingly, coherent interlayer transport strongly reminiscent of superconductivity can be transiently induced up to room temperature (300 kelvin) in YBa2Cu3O6+x (refs 9, 10). Here we report the crystal structure of this exotic non-equilibrium state, determined by femtosecond X-ray diffraction and ab initio density functional theory calculations. We find that nonlinear lattice excitation in normal-state YBa2Cu3O6+x at above the transition temperature of 52 kelvin causes a simultaneous increase and decrease in the Cu-O2 intra-bilayer and, respectively, inter-bilayer distances, accompanied by anisotropic changes in the in-plane O-Cu-O bond buckling. Density functional theory calculations indicate that these motions cause drastic changes in the electronic structure. Among these, the enhancement in the character of the in-plane electronic structure is likely to favour superconductivity.

Direct spectroscopic evidence for phase competition between the pseudogap and superconductivity in Bi2Sr2CaCu2O(8+δ)

In the high-temperature (T(c)) cuprate superconductors, a growing body of evidence suggests that the pseudogap phase, existing below the pseudogap temperature T*, is characterized by some broken electronic symmetries distinct from those associated with superconductivity. In particular, recent scattering experiments have suggested that charge ordering competes with superconductivity. However, no direct link of an interplay between the two phases has been identified from the important low-energy excitations. Here, we report an antagonistic singularity at T(c) in the spectral weight of Bi2Sr2CaCu2O(8+δ) as compelling evidence for phase competition, which persists up to a high hole concentration p ~ 0.22. Comparison with theoretical calculations confirms that the singularity is a signature of competition between the order parameters for the pseudogap and superconductivity. The observation of the spectroscopic singularity at finite temperatures over a wide doping range provides new insights into the nature of the competitive interplay between the two orders and the complex phase diagram near the pseudogap critical point.

Persistence of the superconducting condensate far above the critical temperature of YBa2(Cu,Zn)3O(y) revealed by c-axis optical conductivity measurements for several Zn concentrations and carrier doping levels

The superconductivity precursor phenomena in high temperature cuprate superconductors is studied by direct measurements of the superconducting condensate with the use of the c-axis optical conductivity of YBa2(Cu1-xZnx)3Oy for several doping levels (p) as well as for several Zn concentrations. Both the real and imaginary parts of the optical conductivity clearly show that the superconducting carriers persist up to the high temperatures Tp that is higher than the critical temperature Tc but lower than the pseudogap temperature T*. Tp increases with reducing doping level like T*, but decreases with Zn substitution unlike T*.

Synchrotron radiation-based far-infrared spectroscopic ellipsometer with full Mueller-matrix capability

We developed far-IR spectroscopic ellipsometer at the U4IR beamline of the National Synchrotron Light Source in Brookhaven National Laboratory. This ellipsometer is able to measure both, rotating analyzer and full-Mueller matrix spectra using rotating retarders, and wire-grid linear polarizers. We utilize exceptional brightness of synchrotron radiation in the broad spectral range between about 20 and 4000 cm(-1). Fourier-transform infrared (FT-IR) spectrometer is used for multi-wavelength data acquisition. The sample stage has temperature variation between 4.2 and 450 K, wide range of θ-2θ angular rotation, χ tilt angle adjustment, and X-Y-Z translation. A LabVIEW-based software controls the motors, sample temperature, and FT-IR spectrometer and also allows to run fully automated experiments with pre-programmed measurement schedules. Data analysis is based on Berreman's 4 × 4 propagation matrix formalism to calculate the Mueller matrix parameters of anisotropic samples with magnetic permeability μ ≠ 1. A nonlinear regression of the rotating analyzer ellipsometry and∕or Mueller matrix (MM) spectra, which are usually acquired at variable angles of incidence and sample crystallographic orientations, allows extraction of dielectric constant and magnetic permeability tensors for bulk and thin-film samples. Applications of this ellipsometer setup for multiferroic and ferrimagnetic materials with μ ≠ 1 are illustrated with experimental results and simulations for TbMnO3 and Dy3Fe5O12 single crystals. We demonstrate how magnetic and electric dipoles, such as magnons and phonons, can be distinguished from a single MM measurement without adducing any modeling arguments. The parameters of magnetoelectric components of electromagnon excitations are determined using MM spectra of TbMnO3.

Origin of the magnetic field induced changes of the transverse plasma mode in the c-axis infrared response of underdoped YBa2Cu3O(7-δ)

We report on results of our theoretical study of magnetic field induced changes of the c-axis infrared response of bilayer cuprate superconductors using the phenomenological multilayer model involving the conductivity of the spacing layers and that of the bilayer units. For H perpendicular to the planes, the local conductivities have been expressed in terms of a two-fluid approximation--as weighted averages of the superconducting state ones and the normal state ones representing contributions of the vortex cores, the weight of the latter increasing linearly with the field. This allows us to reproduce and interpret the fast decrease with increasing H of the well known 400 cm(-1) peak (transverse plasma mode) in the c-axis conductivity, observed by LaForge and co-workers. For the local conductivities of underdoped YBa(2)Cu(3)O(7-δ) with T(c)=58 K reported by Dubroka and co-workers and the fraction of the normal state (T ≈ T(c)) component given by (μ(0)H/25 T), the computed field induced changes of the reflectivity are in quantitative agreement with the data. This suggests that the response at H=0 and T ≈ T(c) is close to that at H=25 T < H(c2) and T ≪ T(c), in accord with theories attributing the above T(c) state to that of a superconductor lacking long-range phase coherence. Also discussed are changes of the response induced by H parallel to the CuO(2) planes.

Evidence of a precursor superconducting phase at temperatures as high as 180 K in RBa2Cu3O(7-δ) (R=Y, Gd, Eu) superconducting crystals from infrared spectroscopy

We show that a multilayer analysis of the infrared c-axis response of RBa2Cu3O(7-δ) (R=Y, Gd, Eu) provides important new information about the anomalous normal-state properties of underdoped cuprate high temperature superconductors. In addition to competing correlations which give rise to a pseudogap that depletes the low-energy electronic states below T*≫T(c), it enables us to identify the onset of a precursor superconducting state below T(ons)>T(c). We map out the doping phase diagram of T(ons) which reaches a maximum of 180 K at strong underdoping and present magnetic field dependent data which confirm our conclusions.

Evidence for two competing order parameters in underdoped cuprate superconductors from a model analysis of Fermi-Arc effects

Preformed pairs above T{c} and the two-gap scenarios are two main proposals for describing the low-doping pseudogap phase of high-T{c} cuprates. Very recent angle-resolved photoemission experiments have shown features which were interpreted as evidence for preformed pairs. Here it is shown that those results can be explained also in the context of the two-gap scenario if self-energy effects are considered. The discussion is based on the d charge-density wave theory or the flux phase of the t-J model.

Sum rules and interlayer infrared response of the high temperature YBa2Cu3Oy superconductor in an external magnetic field

We present infrared magneto-optical measurements of the c-axis conductivity of YBa2Cu3Oy in both the underdoped (y=6.67 and 6.75) and optimally doped (y=6.95) regimes. We show that modest c-axis magnetic fields radically modify the condensate formation and restore conventional BCS-like energetics. Additionally, we demonstrate the pivotal role of interplane coherence in the anomalous high-energy contribution to the superfluid density.

Superconducting energy gap and c-axis plasma frequency of (Nd,Sm)FeAsO0.82F0.18 superconductors from infrared ellipsometry

We present far-infrared ellipsometric measurements of polycrystalline samples of the pnictide superconductor RFeAsO0.82F0.18 (R=Nd and Sm). We find evidence that the electronic properties are strongly anisotropic such that the optical spectra are dominated by the weakly conducting c-axis response similar to the cuprate high-temperature superconductors. We deduce an upper limit of the c-axis superconducting plasma frequency of omega pl,c(SC)< or =260 cm(-1) corresponding to a lower limit of the c-axis magnetic penetration depth of lambda c > or =6 microm and lambda c/lambda ab > or =30 as compared to lambda ab=185 nm from muon spin rotation [A. Drew, arXiv:0805.1042 [Phys. Rev. Lett. (to be published)]]. We also observe a gaplike suppression of the conductivity in the superconducting state with a shoulderlike feature at omegaSC* approximately 300 cm(-1) and spectral shape which is consistent with an unconventional order parameter with 2Delta approximately omegaSC* approximately 37 meV.